According to the latest financial reports from a sporting goods store, the mean sales per customer was $75 with a population standard deviation of $6. The store manager believes 39 randomly selected customers spent more per transaction. What is the probability that the sample mean of sales per customer is between $76 and $77 dollars? You may use a calculator or the portion of the z -table given below. Round your answer to two decimal places if necessary.

13.04% probability that the sample mean of sales per customer is between $76 and $77 dollars.

Step-by-step explanation:

To solve this problem, we have to understand the Normal Probability Distribution and the Central Limit Theorem.

Normal probability distribution:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean and standard deviation , the zscore of a measure X is given by:

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central limit theorem:

The Central Limit Theorem estabilishes that, for a random variable X, with mean and standard deviation , a large sample size, of at least 30, can be approximated to a normal distribution with mean and standard deviation

In this problem, we have that:

What is the probability that the sample mean of sales per customer is between $76 and $77 dollars?

This is the pvalue of Z when X = 77 subtracted by the pvalue of Z when X = 76. So

X = 77

By the Central Limit Theorem

has a pvalue of 0.9812

X = 76

has a pvalue of 0.8508

0.9812 - 0.8508 = 0.1304

13.04% probability that the sample mean of sales per customer is between $76 and $77 dollars.

it is c, trust i got your back lol

step-by-step explanation:

answer: h

step-by-step explanation: